Clusters of galaxies, as the largest virialized systems in the Universe, are ideal laboratories to study the formation and evolution of cosmic structures. The luminous matter of clusters consists of galaxies and of an embedding intracluster medium (ICM), which has been heated to temperatures of tens of millions degrees, and thus is detected through its thermal emission in the soft X-ray regime. Most of the detailed knowledge of galaxy clusters has been obtained in recent years from the study of ICM through X-ray Astronomy. At the same time, radio observations have proved that the ICM is mixed with non-thermal components, i.e. highly relativistic particles and large-scale magnetic fields, detected through their synchrotron emission.The knowledge of the properties of these non-thermal ICM components has increased significantly, owing to sensitive radio images and to the development of theoretical models. Diffuse synchrotron radio emission in the central and peripheral cluster regions has been found in many clusters. Moreover large-scale magnetic fields appear to be present in all galaxy clusters, as derived from Rotation Measure (RM) studies. Non-thermal components are linked to the cluster X-ray properties, and to the cluster evolutionary stage, and are crucial for a comprehensive physical description of the intracluster medium. They play an important role in the cluster formation and evolution.We review here the observational properties of diffuse non-thermal sources detected in galaxy clusters: halos, relics and mini-halos. We discuss their classification and properties. We report published results up to date and obtain and discuss statistical properties. We present the properties of large-scale magnetic fields in clusters and in even larger structures: filaments connecting galaxy clusters. We summarize the current models of the origin of these cluster components, and outline the improvements that are expected in this area from future developments thanks to the new generation of radio telescopes.

Aims. The aim of the present work is to constrain the Coma cluster magnetic field strength, its radial profile and power spectrum by comparing Faraday rotation measure (RM) images with numerical simulations of the magnetic field. Methods. We have analyzed polarization data for seven radio sources in the Coma cluster field observed with the Very Large Array at 3.6, 6 and 20 cm, and derived Faraday rotation measures with kiloparsec scale resolution. Random three dimensional magnetic field models have been simulated for various values of the central intensity B 0 and radial power-law slope η, where η indicates how the field scales with respect to the gas density profile. Results. We derive the central magnetic field strength, and radial profile values that best reproduce the RM observations. We find that the magnetic field power spectrum is well represented by a Kolmogorov power spectrum with minimum scale ∼2 kpc and maximum scale ∼34 kpc. The central magnetic field strength and radial slope are constrained to be in the range (B 0 = 3.9 μG; η = 0.4) and (B 0 = 5.4 μG; η = 0.7) within 1σ. The best agreement between observations and simulations is achieved for B 0 = 4.7 μG; η = 0.5. Values of B 0 > 7 μG and <3 μG as well as η < 0.2 and η > 1.0 are incompatible with RM data at 99% confidence level.

The radio spectral index map of the Coma halo shows a progressive steepening of the spectral index with increasing radius. Such a steepening cannot be simply justified by models involving continuous injection of fresh particles in the Coma halo or by models involving diffusion of fresh electrons from the central regions. We propose a two‐phase model in which the relativistic electrons injected in the Coma cluster by some processes (starbursts, AGNs, shocks, turbulence) during a first phase in the past are systematically reaccelerated during a second phase for a relatively long time (∼1 Gyr) up to the present time. We show that for reacceleration time‐scales of ∼0.1 Gyr this hypothesis can well account for the radio properties of Coma C. For the same range of parameters which explain Coma C we have calculated the expected fluxes from the inverse Compton scattering of the Cosmic Microwave Background (CMB) photons, finding that the hard X‐ray tail discovered by BeppoSAX may be accounted for by the stronger reacceleration allowed by the model. The possibility of extending the main model assumptions and findings to the case of the other radio haloes is also discussed, the basic predictions being consistent with the observations.

Abstract. We present a numerical approach to investigate the relationship between magnetic fields and Faraday rotation effects in clusters of galaxies. We can infer the structure and strength of intra-cluster magnetic fields by comparing our simulations with the observed polarization properties of extended cluster radio sources such as radio galaxies and halos. We find the observations require a magnetic field which fluctuates over a wide range of spatial scales (at least one order of magnitude). If several polarized radio sources are located at different projected positions in a galaxy cluster, as is the case for A119, detailed Faraday rotation images allow us to constrain both the magnetic field strength and the slope of the power spectrum. Our results show that the standard analytic expressions applied in the literature overestimate the cluster magnetic field strengths by a factor of ∼2. We investigate the possible effects of our models on beam depolarization of radio sources whose radiation traverses the magnetized intracluster medium. Finally, we point out that radio halos may provide important information about the spatial power spectrum of the magnetic field fluctuations on large scales. In particular, different values of the index of the power spectrum produce very different total intensity and polarization brightness distributions.